Spatiotemporal Kronecker Covariance Neural Networks

Real-world traffic data exhibit heterogeneous spatial correlations and nonlinear temporal dynamics, posing substantial challenges for accurate spatio-temporal forecasting. Existing approaches have developed increasingly sophisticated graph, attention, and decomposition architectures, while the influence of the underlying nonlinear function approximator has received comparatively less attention. In this work, we propose STKAN, a spatio-temporal forecasting architecture that introduces Taylor-polynomial Kolmogorov--Arnold Network modules into spatial and temporal token mixing. STKAN first constructs high-level spatial representations through a learnable soft node-group assignment mechanism, applies group-wise spatial mixing, and subsequently models temporal dependencies over the compressed sequence. Spatial and temporal self-attention layers are further employed to capture long-range interactions. Experiments on five traffic forecasting benchmarks show that STKAN achieves competitive performance and performs better than the evaluated MLP-based variant in the tested settings. These results suggest that the design of nonlinear function approximators can serve as a useful complement to architectural design in spatio-temporal forecasting.

Multivariate time series forecasting is fundamental to numerous domains such as energy, finance, and environmental monitoring, where complex temporal dependencies and cross-variable interactions pose enduring challenges. Existing Transformer-based methods capture temporal correlations through attention mechanisms but suffer from quadratic computational cost, while state-space models like Mamba achieve efficient long-context modeling yet lack explicit temporal pattern recognition. Therefore we introduce UniMamba, a unified spatial-temporal forecasting framework that integrates efficient state-space dynamics with attention-based dependency learning. UniMamba employs a Mamba Variate-Channel Encoding Layer enhanced with FFT-Laplace Transform and TCN to capture global temporal dependencies, and a Spatial Temporal Attention Layer to jointly model inter-variate correlations and temporal evolution. A Feedforward Temporal Dynamics Layer further fuses continuous and discrete contexts for accurate forecasting. Comprehensive experiments on eight public benchmark datasets demonstrate that UniMamba consistently outperforms state-of-the-art forecasting models in both forecasting accuracy and computational efficiency, establishing a scalable and robust solution for long-sequence multivariate time-series prediction.

Spiking Neural Networks (SNNs) have emerged as an energy-efficient alternative to conventional neural networks, demonstrating strong performance in computer vision and robotics. More recently, SNNs have been applied to time series forecasting (TSF), with methods exploring spiking temporal backbones, spike-compatible positional encodings, Fourier-domain processing, and redesigned neuron dynamics. However, existing SNN forecasting approaches process variables independently, lacking explicit mechanisms for modeling inter-variable dependencies. This is a critical limitation in multivariate settings, where cross-variable correlations carry substantial predictive information. We propose Spiking Fourier Graph Operators (SpikF-GO), which addresses this gap by combining a hypervariate graph formulation in which every scalar observation becomes a graph node with spike-driven spectral processing. SpikF-GO introduces a Hard Concrete frequency gate for learnable sparse frequency selection and a Complex LIF gate that applies independent spiking neurons to real and imaginary Fourier components, preserving binary, event-driven computation throughout the spectral domain. We further present a variant incorporating Central Pattern Generator-based positional encodings for stronger long-range temporal modeling. Evaluated on eight benchmarks under a unified experimental protocol, SpikF-GO achieves the best average rank among all SNN methods and outperforms its ANN counterpart, FourierGNN, at reduced energy cost. SpikF-GO maintains competitive accuracy even at substantially smaller embedding dimensions, thereby achieving significant energy reductions. To our knowledge, this is among the first works to bring graph-based multivariate modeling into the spiking domain for TSF and the first to provide a unified comparison across SNN forecasting architectures under a common experimental protocol.